# Thread: Mean & Variance Problem... (Any hints or help will do)

1. ## Mean & Variance Problem... (Any hints or help will do)

X1and X2 are independently distributed random variables with
P(X1 = Z+1 ) = P(X1 = Z-1 ) = 1/2
P(X2 = Z-2 ) = P(X2 = Z+2 ) = 1/2.
Find the value of a and b which minimize the variance of Y = aX1 + bX2 subject to the condition that E[Y] = Z.
What is the minimum value of this variance?

2. V(X1)=1 and V(X2)=4

The constraint since E(X1)=z=E(X2) is a+b=1, where z should be lower case, not upper case.

So use calc 1 to minimize $a^2 +4b^2$ given a+b=1, by inserting one of these two variables,a,b.

You could use LaGrange, but cal 1 is easier.

I get a=4/5, b=1/5 giving me 20/25=.8 as the answer.